Ha! Same here! I though that it must be something like that link between relief of depression and sleep deprivation. Turns out, fitful is not related to being fit or to a full night of sleep, but more to throwing a fit.

I can see how it'd be interpreted that way at first glance. My read was always that it meant "full of fits", in the way that a child throws a fit or tantrum. So if your sleep is doing that, it's not good.